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1 GSD VIS Digital Media II - Topics in Parametric and Generative Geometry and Modeling Fall :00AM - 1:00PM Monday, Room 111 (Lectures and Workshops) Andrew Witt awitt@gsd.harvard.edu Office hours: Monday 1PM-2PM on appointment Teaching Fellow/Assistants: Joelle Bitton, Patrica Correa This class explores the design and science of logical form making, examined through geometry, parametric control, algorithms, and digital tools. The point of departure is a cumulative sequence of fundamental topics and problems in design geometry which have recurring impact on the history of form. These problems will provide a context and pretext for a rigorous introduction to parametric modeling, algorithmic automation, and the mathematical principles underpinning them. These logical investigations of modeling will cultivate a certain objective approach to form that explores the application of parametric approaches that are both deductive (for example, topological classifications, surface characteristics, and pattern logics) and empirical (for example, material deformation and generative detailing). Thematically, the course will foster an integrated understanding of topics such as parametric geometry definition, surface geometry qualification, and the converse dynamics of packing and subdivision. As a part of the course, students will learn to use parametric design tools Rhino Grasshopper, Python, and Digital Project, supplemented by other tools to interrogate and permute these design problems. Through a series of lectures, software tutorials, and mathematical workshops students will respond to the fundamental design problems with a progression of digital design modeling exercises culminating in a final project which will demonstrate appropriate synthesis of design ambition, mathematical characterization, and parametric control. Format The class will be a weekly 3-hour session divided into a lecture half and software and geometry/ computation workshop half. The class will be organized thematically, with each theme encompassing certain historical, technical, and formal principles. Evaluation Students will be evaluated through a series of four assignments, including a final project.

2 Schedule: Class Date Lecture Topic Workshop Topic Monday, Sept. 09, 2013 Introduction Mathematics of Geometry, Python I Monday, Sept. 16, 2013 Patterns, Symmetry, Topology Python II Monday, Sept. 23, 2013 Curves and Curvature Grasshopper I Monday, Sept. 30, 2013 Surface Geometry Surface Control, Grasshopper II Monday, Oct. 07, 2013 Surfaces and Topology I Grasshopper III Monday, Oct. 14, 2013 Surfaces and Topology II Grasshopper IV + Python Monday, Oct. 21, 2013 Subdivisions and Packings I Digital Project I + Formulas Monday, Oct. 28, 2013 Parametric Modules Digital Project II + Powercopies Monday, Nov. 04, 2013 Subdivisions and Packings II Digital Project III + Knowledge Patterns Monday, Nov. 11, 2013 Constraints and Embedded Digital Project IV + Rules, Analysis Rules Monday, Nov. 18, 2013 Combinatorics and Optimization, Galapagos Optimization Monday, Nov. 25, 2013 Data-driven Design Datasheets, Automated File I/O Monday, Dec. 02, 2013 Building Information Modeling BIM, Data Extraction Monday, Dec.16, 2013 Final Review (Tentative) Assessment: Grades will be evaluated based on the formal and experimental ambition of assignments, the conceptual clarity, cleverness, and precision of the execution, and the mastery of technical concepts as evidenced by submitted models, review interactions, and class participation. 20% Attendance. 40% Interim assignments 40% Final assignment September 09, Introduction Problem: What is design computation? This class introduces the broad topics and themes of the class in overview, including general problems and concepts of architectural geometry. Theoretical topics: Sets and numeric functions, weights and distributions, vectors. Technical topics: Python basics; variables, loops, conditionals

3 Carpo, Mario and Frederique Lemerle. Perspective, Projections, and Design: Technologies of Architectural Representation. New York: Routledge, Edwards, Lawrence. Projective Geometry. Edinburgh: Floris Books, Monge, Gaspard. Geometrie Descriptive. Paris: Baudoin, Pedoe, Daniel. Geometry: A Comprehensive Course. London: Cambridge University Press, Architectures Non-Standard. Paris: Centre Georges Pompidou, Legendre, George. Architectural Design: The Mathematics of Space. London: Wiley, September 16, Patterns, Symmetry, Pattern Topology Problem: What are the basic descriptors of 2-dimensional patterns? This class examines the fundamental symmetry patterns, both geometry and topological, that ascribe structure to 2-dimensional patterns. Theoretical topics: Topological and geometric symmetries, symmetry groups, topological exceptions, bi-arcs, graphs. Technical topics: Rhino Python. Points, lines, polylines, curves, patterns. Assignment: Assignment 01 given Kauffman, Louis. On Knots. Princeton: Princeton University Press, September 23, Curves and Curvature - Assignment 01 Due Problem: How does one represent and manipulate curves in space? This class examines the geometric and historical range of architectural surface types. Theory and construction methods for developable, spanning, and medial surfaces will be introduced. The class will particularly focus on surfaces which can be constructed from flat or singly-curved material. Theoretical topics: parametric curves, conic sections, NURBS curves, osculating circles, involutes and evolutes, osculating tangent and normal planes, torsion, mono- bi- and tri-tangencies, Biarc discretization. Technical topics: Introduction to Grasshopper.

4 Assignment: Assignment 01 due, assignment 02 given Burry, Mark. The New Mathematics of Architecture. London: Thames & Hudson, Piegl, Les and Wayne Tiller. The NURBS Book. September 30, Surface Geometry Problem: How does one represent, design, and build parametric surfaces? This class examines the geometric and historical range of architectural surface types. Theory and construction methods for developable and ruled surfaces will be introduced, including metrics for the measurement and quantification or such surfaces. The class will particularly focus on surfaces which can be constructed from flat or singly-curved material. Theoretical topics: Surface intersections, ruled surfaces, developable surfaces, affine developables, rectifying and tangent developables, curvature measures, implicit surfaces, kinetic surfaces. Technical topics: Grasshopper II. Assignment: Continue assignment 02 Lynn, Greg. Folding in Architecture. London: Wiley, Toponogov, Victor Andreevich. Differential geometry of curves and surfaces. Boston : Birkhauser, Shelden, Dennis R. Digital surface representation and the constructibility of Gehry's architecture. Cambridge: MIT, October 07, Surface and Topology I Problem: What are the methods to build topologically complex surfaces? This class considers the notion of surface topology and explores categories of surfaces that could be considered topologically complex. Particular care will be taken to examine surfaces that have specific architectural implications in terms of organization of constructability. Theoretical topics: Subdivision surfaces, offset surfaces, spanning surfaces, knot complexes, topological surfaces, medial surfaces.

5 Technical topics: Grasshopper III Assignment: Continue Assignment 02 Burry, Mark. The New Mathematics of Architecture. London: Thames & Hudson, October 14, Surface and Topology II - Assignment 02 Due Problem: What are the methods to build topologically complex surfaces? This class continues to examine topological surfaces, including surface maps and metrics for subdivision. Theoretical topics: Subdivision surfaces, offset surfaces, spanning surfaces, knot complexes, topological surfaces, medial surfaces. Technical topics: Grasshopper IV Assignment: Assignment 02 due, Assignment 03 and Final Project given. Burry, Mark. The New Mathematics of Architecture. London: Thames & Hudson, October 21, 2013 Subdivisions and Packings I Problem: How can planes, surfaces, and spaces be filled and patterned? This class surveys the modes of tessellation possible for planes, surfaces, and spaces, with particular attention to implicit constraints on these partitions. Theoretical topics: Space packings, topological graph structures. Technical topics: Digital Project I Assignment: Continue Assignment 03 October 28, 2013 Parametric Modules Problem: How can the detailing of nonstandard components be automated?

6 This class builds on the previous one to elaborate basic techniques for automation and modular surface effects. It also examines methods for embedding drawings, quantitative analysis, and fixation details into adaptive components. Examples from practice of generative detailing will be presented. Theoretical topics: Modularization, encapsulation, components. Technical topics: Digital Project II Assignment: Continue Assignment 03 November 04, Subdivisions and Packings II - Assignment 03 Due Problem: How can in irregular (2D or 3D) shape be smoothly patterned? This class examines the converse logics of subdivision and packing in the context of surfaces and spaces. Particular attention will be paid to invariants that help to classify the structure of forms and subdivide them in an ordered and formally determinate way. The class also introduces methods for the automated articulation of surfaces and basic data extraction. Examples from practice of the generation of subdivisions will be presented. Theoretical topics: Graphs, curve skeletons, topology of circle packing, orthotropic and nonorthotropic armatures, wrapping curves, reflect lines, ruling lines, geodesics, lines of curvature, modular subdivisions, polytopes, cellular growth, space packings. Technical topics: Digital Project III Assignment: Assignment 03 due Meredith, Michael. From Control to Design. New York : Actar, November 11, 2013 Constraints and Embedded Rules Problem: How can rules of a fabrication or design process be embedded in a 3D model? This class considers how responsive and adaptive rules can written and deployed in parametric models. Implicit rules, explicit rules, and constraints will be contextualized with case studies. Theoretical topics: Rule sets, constraint-based design, economies of fabrication and process. Technical topics: Digital Project IV Assignment: No assignment, continue work on assignment 03.

7 Legendre, George L. Architectural Design : The Mathematics of Space. London: Wiley, November 18, 2013 Combinatorics and Optimization Problem: What is design optimization? This class considers the tools and techniques used to generate viable alternatives and to achieve a design optimum. The underlying frameworks and assumptions that make optimization plausible will be explored in a critical context. Single-objective and multi-objective optimizations will be considered in detail, as well as broader questions on the theory of design optimization. Theoretical topics: Genetic algorithms, global and local optimization, gradient-based and simulated annealing techniques. Technical topics: Galapagos and Digital Project Optimizer. Assignment: Final assignment presented. November 25, 2013 Data-driven Design Problem: How can numeric and quantitative information inform the design process? This class investigates the use of existing or generated data sets to inform design. These data sets are either tabular information or databases, and the use of these sets is often central to the use of parametric models with specialist consultants. Theoretical topics: Data formats, using data sets with parametric models, integration with simulation tools. Technical topics: Datasheets, data file input. December 02, 2013 Building Information Models Problem: How can construction processes be integrated around 3D models? This class surveys the problems and themes of building information modeling. Here BIM is considered broadly, and includes integrated approached to bidding, construction, assembly, and

8 geometric control. The common BIM packages will be introduced and examined, and the practical impact of BIM explored. Theoretical topics: Organization problems of design, new contracting methods, integrated project delivery, Revit, model servers. Technical topics: BIM tools and processes. Eastman, Chuck. BIM Handbook: A Guide to Building Information Modeling for Owners, Managers, Designers, Engineers and Contractors. New York: Wiley, December 16, Final Review - Final Assignment Due Summary: The final review will require the production of a model, generative detail drawings, and analytic statistics of your design. You may optionally include an analytic animation to describe the parametric behavior of the model.